But her campaign has no record of them. Instead, volunteers and staff with the super PAC CARLY for America handed out stickers and signed up the attendees to receive more information. (Due to a ruling by the Federal Election Commission, the super PAC's use of "Carly" has to be an acronym, so it is not too similar to her campaign's official name, Carly for President. CARLY stands for "Conservative Authentic Responsive Leadership for You.")
This is how Fiorina, who has rocketed to the top tier in national polls since last week's CNN debate, is organizing in Iowa.
"I would say most of the organizing work is done on CARLY for America," campaign state director Christopher Rants told CNN on Wednesday. On the campaign side, he said, "Our focus has always been to put Carly in front of as many Iowans as possible."
That includes holding and advertising public events with Fiorina where the super PAC, which is not allowed to coordinate with the campaign, can freely attend, harvest attendees' names and contact information, and distribute information on the candidate.
Many of the attendees at the Davenport event said they intended to caucus for Fiorina on Feb. 1.
With participation in the Republican debates being determined by candidates' standing in national polls, many candidates are not spending as much time in early states like Iowa and are leaving it to their super PACs to recruit volunteers and get their message out, said Timothy Hagle, a political science professor at the University of Iowa.
Up until the 2016 cycle, campaigns were largely responsible for grassroots organizing. Super PACs are now testing the waters and taking on a larger role, particularly in early-voting states.
Asked repeatedly by reporters about her organization and super PAC after the event, Fiorina said her campaign would have the money and the organization it needs to win and that it is not a problem that she is relying so much on her super PAC to provide organization and a political infrastructure for her campaign on the ground here.
"We publicize every event on my schedule and anyone can come," she told reporters after Friday's town hall event. "What you see happening is a super PAC is organizing people. We're not coordinating with them. We're not asking them to. I don't know what they're doing, they don't tell us what they're doing."
Hagle said an arrangement like Fiorina's could lead to problems if other candidates challenge what they view as inappropriate coordination between the campaigns and the super PAC.
"I think people will challenge it if they see activities that are inappropriate in terms of coordination," he said. "Democrats, believe me, will mention that and try to get an investigation going with the (Federal Election Commission)."
At the Davenport event, CARLY for America not only signed up attendees interested in learning more about Fiorina, they were the only ones providing literature about the candidate. Asked how that did not represent an in-kind contribution to the campaign, Fiorina told reporters to ask the super PAC.
The super PAC is also taking the lead on grassroots organization. CARLY for America state director Mary Earnhardt said the organization is identifying community captains to get involved as active ambassadors for Fiorina, an important organizing tactic that can be key to mobilizing caucus-goers. Volunteers for CARLY for America walk in parades, hand out stickers, and speak at events on Fiorina's behalf.
"My team and I are Carly's biggest cheerleaders in the state of Iowa. We spread her message, all the way, central committee meetings and county Republican fundraisers. We go to all sorts of different events and just talk about Carly and why we're supporting Carly. We're just helping to build the buzz," Earnhardt said.
Fiorina has a bare-bones campaign staff of two in the first-in-the-nation caucus state, whereas the CARLY for America super PAC has eight, according to the campaign and the super PAC's state directors, respectively.
The lines of coordination can often seem blurred and confusing to both voters and reporters. On Wednesday evening in Des Moines, dozens of supporters lined up to see the CARLY for America-produced "Citizen Carly" documentary at a local movie theater. They were greeted by her husband Frank Fiorina, who personally thanked each attendee. Most attendees, when asked by CNN, did not know that the event was sponsored by the PAC and not the campaign, and most didn't seem to care.
The challenge for super PAC CARLY for America is organizing effectively without any communication from the campaign.
Another question for campaigns that rely heavily on volunteers is whether that kind of organization will be adequate to get folks out on caucus night.
Fiorina's base of support in Iowa ranges from tried-and-true Iowa activists to first-time caucus-goers. Asked whether CARLY for America has been focused on caucus education for those who may not have been politically active before, Earnhardt said, "Oh, it's only September."
"I think a lot of people in Iowa know about the caucus, which is fortunate, but absolutely, I mean, we'll help anybody who has questions about it," she said.
Political observers in Iowa note that Rick Santorum won the caucuses last time around without a lot of staff or money -- proof that a strong and enthusiastic network of volunteers can pick up the slack if a candidate lacks a large campaign apparatus. This is the very definition of an effective grassroots campaign.
"You can do very well by word of mouth," said Steffen Schmidt, a political science professor at Iowa State University, who believes the focus on Fiorina's ground game in Iowa at this stage of the race is overblown. Schmidt says the former CEO has plenty of time before the Feb. 1 contest to gain the necessary support.
"She's in a great spot," Schmidt said. "If you start organizing when you're down at 5%, you're wasting your money."
"You don't set up huge ground organization until you have your message together and are doing well in the polls. Look at what happened to (Scott) Walker," he said, referring to the now-former candidate's outsized Iowa staff.
For now, Fiorina appears to have no plans to change her approach in the Hawkeye State or elsewhere. Her campaign did not directly respond to questions about plans to open offices or to staff up here.
"We're going to keep doing what we've been doing. We don't usually participate in process stories," said campaign press secretary Anna Epstein. "We'll continue traveling the country to meet with voters and answer their questions."